This is a problem that will come up anytime you are changing IP's often on a VPN, especially if you are changing from country to country. This is a red flag in terms of security, for example, your credentials were harvested and sold on the dark web and someone from another country is attempting to breach your account.
Many sites are now, in essence, "forcing" two factor authentication through methods like this that require a code be provided if a login is deemed suspicious. Even if you don't explicitly want this type of verification, it's swiftly becoming the norm and best practice for protecting users.
Have you tried using an authentication app for this, rather than your phone number? This would enable you to pull up the app and use the code provided there instead of providing your phone number to receive a text message.
But the main point is that when you see this, it's security in action, and will likely continue to happen if you are switching IP's and geographic locations often, and not directly the fault of your VPN. You may be able to disable these extra security steps if you really want to, depending on the site or service.
On a side note, a positive way to look at these prompts is that, while they are annoying, your VPN is doing its job. These sites are unsure of who you are -- the exact thing you are trying to accomplish by using software to protect your privacy -- but it's also why they may be asking for security verification
